Question: Express this quotient in scientific notation: ${\frac{3.680\times 10^{3}} {4.0\times 10^{4}}}$
Explanation: Start by collecting like terms together. $= {\frac{3.680} {4.0}} \times{\frac{10^{3}} {10^{4}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.92 \times 10^{3\,-\,4}$ $= 0.92 \times 10^{-1}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.92$ is the same as $9.20 \div 10$ , or $9.20 \times 10^{-1}$ $ = {9.20 \times 10^{-1}} \times 10^{-1} $ $= 9.20\times 10^{-2}$